A Fractal for Valentine’s Day

With Valentine’s Day coming soon, here’s a quick tutorial on how you can create a heart-shaped fractal using the open-source program Apophysis (download it for free here).

1. After opening Apophysis, click on the Transform Editor button:

Transform Editor

In the Transform Editor, click on the New Blank Flame button:

Blank Flame

The Transform Editor window should look like this:

Editor Window

That red triangle you see is called a transform, and we can create all kinds of different effects by changing the values of the Variations. The window in the upper right lets us see a preview of our fractal.

2. In the Variation pane, set the linear value to 0 and the blur value to 0.5. The color of your fractal in the preview window may be different than the one below, and that is fine:


3. Add another transform on top of Transform 1 by clicking the “Adds a new triangle” button:

New Triangle

4. For Transform 2, set the linear value to 0, and the sinusoidal value to 20:


5. Add another transform, and for this one set the linear value to 0, and the julian value to 0.8:


6. Now we’re going to add our final transform. Click on the “Enable final transform” button. Set the linear value of this transform to 0, and the juliascope value to 1:


7. We’re almost done! In the Transform Editor, click the “Triangle” tab above the Variations tab.Click the “Up” arrow three times, moving the final transform up 0.3 units. You should see a nice heart!


Here’s what mine looks like in the main window now:


8. You may not like the color of your heart, so let’s delve into the Gradient tool and change the color scheme. In the main window, click on the Gradient button:


Now you have a gradient window to play with! Clicking on the down arrow next to the “Preset” menu makes hundreds of different gradients available:


After you find one you like, you can use the Rotate slider to scroll through the colors within that particular gradient. Clicking the down arrow next to “Rotate” opens a menu that allows you to adjust the hue, brightness, etc.


Clicking the “Camera” tab lets you adjust the position of your fractal.

9. Save your masterpiece by clicking File, then Save Parameters…. Apophysis has a somewhat weird filing system. It will create a directory with a .flame suffix, and save your parameters within that directory. This allows you to save different variations of the same basic fractal within one directory.

10. To save your fractal as a graphics file, click the Render button:


This opens up a window with options to change the size of your image, determine the location of the rendered image file, and set the quality (the higher the number the better). Click the Render button on the bottom right, and sit back and wait. It will render your fractal as a png file.

We’ve just scratched the surface of what Apophysis is capable of. For further exploration, go back to the Transform Editor and tweak the values of the variations for each transform. For example, select Transform 3 and play around with the julian value.Click on the Variables tab and tinker with the julian_power value.


Move the transforms around in the editor’s window, and see what happens. Have fun – there are an infinite variety of fractals just waiting for you to create!

Here’s my final version:

2014 Valentine

This post is inspired by one of the excellent tutorials available at mfcreative, a site that is a fantastic resource for learning how to use Apophysis.


2013 Winterim: Fantastic Fractals

I had a small but talented group of students in my Fractals & Chaos mini-course this year. They used Fractal Explorer, Apophysis, Winfeed, and Chaoscope to create their final projects, which are displayed below. Enjoy!


Fantastic Fractals Final Projects

These are the final projects by the students in my Fantastic Fractals minicourse. After learning the math behind iterated function systems, Julia Sets, and the Mandelbrot Set, they went to work creating their own masterpieces. They used the software Apophysis and Fractal Explorer to generate these beauties.

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Fractals Final Projects

My fractals  minicourse wrapped up last week, and my students have submitted their final projects. They were created using Tierazon and Apophysis. Here are thumbnails of them:

I’m really proud of their work. We began with very simple IFS fractals, and explored some of the features of Apophysis. Then we learned what complex numbers are, and how they are plotted in the complex plane. Once we understood that, we could define what a Julia Set is, and, finally, define the Mandelbrot Set. That’s a lot of math to cover in three weeks.